Answer
$f(x)=-2(x+5)^2(x-4)(x-2)$
Work Step by Step
If $a$ is a zero of a function with multiplicity $b$ then $(x-a)^b$ is a “multiplier” of the function.
Hence here $f(x)=k(x+5)^2(x-4)(x-2)$
$(3,128)$ is on the graph thus $k\cdot(8)^2(-1)(1)=128\\-64k=128\\k=-2$
So $f(x)=-2(x+5)^2(x-4)(x-2)$